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14
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0answers
329 views

Applications of Lawvere's fixed point theorem

Lawvere's fixed point theorem states that in a cartesian closed category, if there is a morphism $A \to X^A$ which is point-surjective (meaning that $\hom(1,A) \to \hom(1,X^A)$ is surjective), then ...
10
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0answers
304 views

Which limit to take as a key applied math decision

The Borel-Kolmogorov paradox refers to situations where non-uniqueness in the notion of conditioning on a set of measure zero leads to apparent contradictions. As a formal matter, one requires ...
3
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0answers
118 views

Reference request: name of a transform

Define a transform on polynomials which is linear and acts on each monomial as $$\widehat{z^k} = \frac{(1+z)(2+z)\ldots(k+z)}{k!}.$$ Does anyone know whether this has a name (and therefore has been ...
3
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0answers
231 views

Seminar Notes Repository

On Seminars, people actually talk a lot more about motivations than when they write in paper. It would be a good idea if there is an online repository where people can upload notes (handwritten, ...
2
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0answers
40 views

Jacobi triple product for multidimensional lattices

The Jacobi triple product identity gives as a special case a product formula for the theta function of a 1-dimensional lattice. Is there a more general product formula for the theta function of an ...
2
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0answers
241 views

Equal signs with fancy marks

Some people use $\stackrel{\mathrm{def}}{=}$, $:=$ or $\stackrel{\Delta}{=}$ for definitions. In more informal contexts, I have also seen $\stackrel{?}{=}$, for "I wish to prove this equality, which ...
1
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0answers
93 views

Reference needed for: Automatic generation of relevant mathematical exercises (similar to ones written by human) with the help of machine learning

I am doing research on automatic generation of relevant mathematical exercises (similar to ones written by human) with the help of machine learning. I have found several research papers on ...
1
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0answers
156 views

Allocation game optimal strategy

There are two players, Alice and Bob. There is an initial pool of 100 dollars. Alice proposes an allocation of the dollars (real numbers, not necessarily integers), and Bob can either accept or ...
1
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0answers
167 views

Finite topological dimension x local compactness

Of course, the two notions are independent one from the other, but often one of them implies the other under some additional hypotheses. For instance: A topological vector space is finite dimensional ...
1
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0answers
163 views

Regarding a Feature of Multivariate Real Function

Any real function can be expressed as a function of the sum of two monotonic real functions? More precisely, for real function p(x, y), there exist continuous real functions P(x), h(x,y), g(x) such ...
0
votes
0answers
70 views

Asymptotic inverses of asymptotic functions

The prime number theorem states that two functions are asymptotic. Their inverses (as functions of an integral variable) are also asymptotic. In general, under what conditions are the inverses of ...
0
votes
0answers
94 views

Repeated function resulting in quadratic time.

Let $$r(f, x) = k$$ such that $$f^k (x) < 2 \hbox{ and } f^{k-1} (x) \geq 2$$ For example $$r(n \rightarrow n-1, 2^n) = 2^n-1; r(n \rightarrow n/2, 2^n) = n.$$ For an arbitrary $c$, we have $$r( ...